norm_snd_le — Mathlib

English

The NNNorm of f.prod g equals the NNNorm of the pair: ||f.prod g||_nn = ||(f, g)||_nn.

Русский

NNNorm произведения равен NNNorm пары: ||f.prod g||_nn = ||(f, g)||_nn.

LaTeX

$$$$\\|f.prod g\\|_{\\!nn} = \\|(f, g)\\|_{\\!nn}.$$$$

Lean4

/-- The operator norm of the second projection `E × F → F` is at most 1. (It is 0 if `F` is zero, so
the inequality cannot be improved without further assumptions.) -/
theorem norm_snd_le : ‖snd 𝕜 E F‖ ≤ 1 :=
  opNorm_le_bound _ zero_le_one (fun ⟨e, f⟩ ↦ by simpa only [one_mul] using le_max_right ‖e‖ ‖f‖)

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